Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 30$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B16 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&116\\104&105\end{bmatrix}$, $\begin{bmatrix}25&98\\16&103\end{bmatrix}$, $\begin{bmatrix}35&64\\44&63\end{bmatrix}$, $\begin{bmatrix}67&56\\4&63\end{bmatrix}$, $\begin{bmatrix}67&64\\52&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.16.dh.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
| 24.96.0-24.r.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.0-24.r.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
| 40.240.8-40.n.2.18 | $40$ | $2$ | $2$ | $8$ | $0$ |
| 120.240.8-40.n.2.8 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.ba.2.7 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.ba.2.19 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.bk.1.10 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.bk.1.17 | $120$ | $2$ | $2$ | $8$ | $?$ |